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Arithmetic Brownian motion and real options


  • Alexander, David Richard
  • Mo, Mengjia
  • Stent, Alan Fraser


We treat real option value when the underlying process is arithmetic Brownian motion (ABM). In contrast to the more common assumption of geometric Brownian motion (GBM) and multiplicative diffusion, with ABM the underlying project value is expressed as an additive process. Its variance remains constant over time rather than rising or falling along with the project’s value, even admitting the possibility of negative values. This is a more compelling paradigm for projects that are managed as a component of overall firm value. After outlining the case for ABM, we derive analytical formulas for European calls and puts on dividend-paying assets as well as a numerical algorithm for American-style and other more complex options based on ABM. We also provide examples of their use.

Suggested Citation

  • Alexander, David Richard & Mo, Mengjia & Stent, Alan Fraser, 2012. "Arithmetic Brownian motion and real options," European Journal of Operational Research, Elsevier, vol. 219(1), pages 114-122.
  • Handle: RePEc:eee:ejores:v:219:y:2012:i:1:p:114-122
    DOI: 10.1016/j.ejor.2011.12.023

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    References listed on IDEAS

    1. De Reyck, Bert & Degraeve, Zeger & Vandenborre, Roger, 2008. "Project options valuation with net present value and decision tree analysis," European Journal of Operational Research, Elsevier, vol. 184(1), pages 341-355, January.
    2. Capozza, Dennis & Li, Yuming, 1994. "The Intensity and Timing of Investment: The Case of Land," American Economic Review, American Economic Association, vol. 84(4), pages 889-904, September.
    3. James E. Smith & Robert F. Nau, 1995. "Valuing Risky Projects: Option Pricing Theory and Decision Analysis," Management Science, INFORMS, vol. 41(5), pages 795-816, May.
    4. Giacometti, Rosella & Teocchi, Mariangela, 2005. "On pricing of credit spread options," European Journal of Operational Research, Elsevier, vol. 163(1), pages 52-64, May.
    5. Brennan, Michael J., 2003. "Corporate investment policy," Handbook of the Economics of Finance,in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 3, pages 167-214 Elsevier.
    6. Capozza, Dennis R & Schwann, Gregory M, 1990. "The Value of Risk in Real Estate Markets," The Journal of Real Estate Finance and Economics, Springer, vol. 3(2), pages 117-140, June.
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    Cited by:

    1. Pedro Godinho, 2015. "Estimating State-Dependent Volatility of Investment Projects: A Simulation Approach," GEMF Working Papers 2015-02, GEMF, Faculty of Economics, University of Coimbra.
    2. Glensk, Barbara & Madlener, Reinhard, 2017. "Evaluating the Enhanced Flexibility of Lignite-Fired Power Plants: A Real Options Analysis," FCN Working Papers 107/2016, E.ON Energy Research Center, Future Energy Consumer Needs and Behavior (FCN).
    3. Ernesto Garnier and Reinhard Madlener, 2016. "The Influence of Policy Regime Risks on Investments in Innovative Energy Technology," The Energy Journal, International Association for Energy Economics, vol. 0(Bollino-M).
    4. Sesana, Debora & Marazzina, Daniele & Fusai, Gianluca, 2014. "Pricing exotic derivatives exploiting structure," European Journal of Operational Research, Elsevier, vol. 236(1), pages 369-381.


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